sin(x+h)-sinx = 2cos(x+h/2)sinh/2请问这个式子是怎样推导出来的?
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![sin(x+h)-sinx = 2cos(x+h/2)sinh/2请问这个式子是怎样推导出来的?](/uploads/image/z/1604881-1-1.jpg?t=sin%28x%2Bh%29-sinx+%3D+2cos%28x%2Bh%2F2%29sinh%2F2%E8%AF%B7%E9%97%AE%E8%BF%99%E4%B8%AA%E5%BC%8F%E5%AD%90%E6%98%AF%E6%80%8E%E6%A0%B7%E6%8E%A8%E5%AF%BC%E5%87%BA%E6%9D%A5%E7%9A%84%3F)
sin(x+h)-sinx = 2cos(x+h/2)sinh/2请问这个式子是怎样推导出来的?
sin(x+h)-sinx = 2cos(x+h/2)sinh/2
请问这个式子是怎样推导出来的?
sin(x+h)-sinx = 2cos(x+h/2)sinh/2请问这个式子是怎样推导出来的?
sin(x+h)-sinx = sinxcosh+cosxsinh-sinx
= sinx(cosh-1)+cosxsinh
= 2cosxsin(h/2)cos(h/2)-2sinxsin^2(h/2)
= 2sin(h/2){cosxcos(h/2)-sinxsin(h/2)}
= 2sin(h/2)cos(x+h/2)
= 2cos(x+h/2)sinh/2